Rationalise the following: { 5 } / { 3 - sqrt(2) }

The aim here is to turn the fraction so that the denominator does not have a surd. 

Given that we know that any surd squared is equal to the number itself, i.e sqrt(2) * sqrt(2) equas 2, or sqrt(x) * sqrt(x) = x we want to use this rule to try to get rid of the { sqrt(2) } in the question above.

Given however that the denominator is { 3 - sqrt(2) }, the only way to get rid of the surd all together is to multiply both the denominator and the numerator by { 3 sqrt(2) }. What we did here is reverse the sign. The sign ensures that the surds cancel when we expand the bracket out.

Original fraction to be rationlised: { 5 } / { 3 - sqrt(2) }

Rationalising: { (5) ( 3 + sqrt(2) ) } / { (3 - sqrt(2) ) ( 3 + sqrt(2) ) }

When you multiply everything out you end up with:

{ 15 + 5*sqrt(2) } / { 7 }

AS
Answered by Amin S. Maths tutor

5590 Views

See similar Maths GCSE tutors

Related Maths GCSE answers

All answers ▸

simplify 7(3y-5) - 2(10 + 4y)


The mean mass of a squad of 19 hockey players is 82 kg A player of mass 93 kg joins the squad. Work out the mean mass of the squad now.


a) Find the equation of the line that passes through (2,10) and (4,16) b) Find the point where the line in (a) intersects the line y=5x-2


Two apples and three bananas cost a total of £1.30. Seven apples and one banana cost a total of £1.70. Find the cost of a) one apple and b) one banana.


We're here to help

contact us iconContact ustelephone icon+44 (0) 203 773 6020
Facebook logoInstagram logoLinkedIn logo

© MyTutorWeb Ltd 2013–2025

Terms & Conditions|Privacy Policy
Cookie Preferences